DSAS - PhD Public Lecture - Kexin Luo

Title: Classification with Measurement Error in Covariates Or Response, with Application to Prostate Cancer Imaging Study

Abstract:

The research is motivated by the prostate cancer imaging study conducted at the University of Western Ontario to classify cancer status using multiple in-vivo images. The prostate cancer histological image and the in-vivo images are subject to misalignment in the co-registration procedure, which can be viewed as measurement error in covariates or response. We investigate methods to correct this problem.

The first proposed method corrects the predicted class probability when the data has misclassified labels.

The correction equation is derived from the relationship between the true response and the error-prone response. The probability for the observed class label is adjusted so it is close to the probability of the true label.  A model can be built with the corrected class probability and the covariates for prediction purpose.

A weighted model method is proposed to construct classifiers with error-prone response. A weight is assigned to each data point according to its position, which indicates the data point's reliability. We propose the weighted models for different machine learning classifiers, such as logistic regression, SVM, KNN and classification tree. The weighted model incorporates the weight for each instance in the model building procedure, and the weighted classifiers trained with the error-prone data can be used for future prediction.

The misalignment in the co-registration procedure can also be treated as measurement error in covariates. A weighted data reconstruction method was proposed to deal with the corrupted covariates.  The proposed method combines two moment reconstruction forms under different assumptions. We incorporated the weights of the data to build adjusted variables to replace the error-prone covariates. The classifiers can be trained on the reconstructed data set. 

Numerical studies were carried out to assess the performance of each method, and the methods were applied to the prostate cancer imaging study. The results show all methods had significantly resolved the misalignment problem.